It really depends on what you're trying to achieve. If you're thinking of adding an amplifier to your factory speakers, you're probably looking to boost the volume and overall sound quality, but that's where things get a bit technical. The amplifier's power rating comes down to how much "push" you want to give your speakers: a 4-channel amplifier around 50-100 watts per channel works great for a decent car audio setup without blowing out your Fiat 500's original system. But if you're planning to add a subwoofer or do a more serious upgrade, then you might be looking at something more powerful, like 200-400 watts total for the subwoofer. The thing is, factory speakers are built to handle a certain amount of power, so pushing it too hard could damage them.
As for the electrical system, that's where it gets tricky. A 2019 500 has a battery and alternator sized for the standard system, and adding a powerful amplifier means you need more power. If you stick with a lightweight amplifier (100-150 watts total), you probably don't need to do anything, but if you go beyond that you should think about upgrading the battery to one with higher amp capacity and maybe also the power cables, which need to be sturdy (not cheap, thin wires) to avoid overheating. A lot of people don't realize this, but the cable from the alternator to the battery and the ground cable are critical: if you use low-quality material, the amplifier won't even reach its true power output and you risk electrical shorts too.
Practical advice: before you buy anything, check how much the audio system you want to add weighs and figure out whether your current cables can support it, or get in touch with a car audio specialist shop in your area. They'll tell you precisely whether you need to tweak your electrical system and what you actually need. It's not a huge expense, but it's better to do it right from the start than to find out later that your amplifier isn't working the way it should.